They are so pretty, I wonder if maybe the goats nibbled on them. Could be. lol
Drakes can be pretty brutal with ducklings I usually keep my mamas and ducklings separated from my drake until they are at least 3 weeks old by then they can get away easier. Hopefully he is just scaring them and not trying to hurt them.
They do look pretty ragged but if not wet feather then a good molt should fix them right up. Lots of good feed along with some extra protein dried meal worms, cat or dog kibble good quality. can help with feather issues too. I think molt is going to do the trick for yours.
I am not sure how old or sexes of ducklings I am thinking about 8 weeks maybe.